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Simplifying 2a2 + 4a + -48 = 2 Reorder the terms: -48 + 4a + 2a2 = 2 Solving -48 + 4a + 2a2 = 2 Solving for variable 'a'. Reorder the terms: -48 + -2 + 4a + 2a2 = 2 + -2 Combine like terms: -48 + -2 = -50 -50 + 4a + 2a2 = 2 + -2 Combine like terms: 2 + -2 = 0 -50 + 4a + 2a2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-25 + 2a + a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-25 + 2a + a2)' equal to zero and attempt to solve: Simplifying -25 + 2a + a2 = 0 Solving -25 + 2a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + 2a + 25 + a2 = 0 + 25 Reorder the terms: -25 + 25 + 2a + a2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 2a + a2 = 0 + 25 2a + a2 = 0 + 25 Combine like terms: 0 + 25 = 25 2a + a2 = 25 The a term is 2a. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2a + 1 + a2 = 25 + 1 Reorder the terms: 1 + 2a + a2 = 25 + 1 Combine like terms: 25 + 1 = 26 1 + 2a + a2 = 26 Factor a perfect square on the left side: (a + 1)(a + 1) = 26 Calculate the square root of the right side: 5.099019514 Break this problem into two subproblems by setting (a + 1) equal to 5.099019514 and -5.099019514.Subproblem 1
a + 1 = 5.099019514 Simplifying a + 1 = 5.099019514 Reorder the terms: 1 + a = 5.099019514 Solving 1 + a = 5.099019514 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + a = 5.099019514 + -1 Combine like terms: 1 + -1 = 0 0 + a = 5.099019514 + -1 a = 5.099019514 + -1 Combine like terms: 5.099019514 + -1 = 4.099019514 a = 4.099019514 Simplifying a = 4.099019514Subproblem 2
a + 1 = -5.099019514 Simplifying a + 1 = -5.099019514 Reorder the terms: 1 + a = -5.099019514 Solving 1 + a = -5.099019514 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + a = -5.099019514 + -1 Combine like terms: 1 + -1 = 0 0 + a = -5.099019514 + -1 a = -5.099019514 + -1 Combine like terms: -5.099019514 + -1 = -6.099019514 a = -6.099019514 Simplifying a = -6.099019514Solution
The solution to the problem is based on the solutions from the subproblems. a = {4.099019514, -6.099019514}Solution
a = {4.099019514, -6.099019514}
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